June 2006
Intermediate to advanced
515 pages
16h 22m
English
Content preview from Applied Mathematical Methods
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Chapter 35
1 Note that, with continuous functions as coefficients, the IVP is well-posed which can be always solved numerically. As such, solutions with required specifications do exist for the ODE and they are genuine functions. But, unfortunately, human mathematics has not yet found a symbolic representation for them. This note is to clarify the apparent dichotomy between the statements “solution exists” and “solution cannot be determined (analytically)”.
2 This is ordinary inner product in n-dimensional Euclidean space, and has nothing to do with the inner product of function space.
3 These two tools are not very efficient in numerical computations in comparison to competing tools, but for this kind of analytical treatments they are quite ...
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